Calculate the quantities demanded of gourmet coffee

Reference no: EM133426077

Question: Consider a hotelling linear city model with 500 consumers with locations uniformly distributed on a street represented by the interval [0, 1]. There are two gourmet coffee stores which are located at x= 0 (store 1) and x= 1 (store 2). Suppose each consumer will buy exactly one unit of coffee from the store for which price plus transportation cost is lower. Assume that the consumers willingness to pay is significantly higher than the prevailing prices, so that it is optimal to buy. The transportation costs are $5 per unit distance and the coffee stores have constant marginal cost of MC=$6. The coffee stores compete in prices.

a) Given the stores' prices p1 and p2, calculate the quantities demanded of gourmet coffee from the stores.

p1 + 5 * x* = p2 + 5 * (1 - x*)

x* = (p2 - p1 + 5) / 10

So demand functions would be

q1 = 50p2-50p1+250

q2 = 50p1-50p2+250

b) Find the Bertrand equilibrium prices.

This part I am not sure. Wouldn't we just find the MR of Q1 and Q2 and set = MC????
Please solve part B and C

c) Illustrate that the coffee stores can increase their profits if they collude and raise their prices with one example.

Reference no: EM133426077

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